RMSprop equation - dividing by a matrix?
Yes, you are correct, $S_{dW}$, in this case, is the matrix/tensor and it will have the same shape as gradient matrix/tensor. The update rule divides each element in gradient to each gradient in $S_{dW}$ or you can say &quot;element-wise division&quot;.
To avoid the zero variable in $S_{dW}$, the equation usually like this:
$$
W=W-\alpha \frac{dW}{\sqrt{S_{dW}+\epsilon}} \text{  where } \epsilon=10^{-8}
$$
If you want to implement it manually with Python, you can take a look at this link